Medical grafting connectors and fasteners

A connector for use in connecting an axial end portion of a tubular medical graft to the side wall of a patient's tubular body tissue conduit so that the lumen of the graft communicates with the lumen of the conduit through an aperture in the side wall of the conduit to permit body fluid flow between the lumens without leakage of body fluid to the outside of the graft and the conduit adjacent the connector comprising:

• an annular structure having first and second axially adjacent substructures, the first substructure being configured to be disposed substantially concentrically inside the axial end portion of the graft and being circumferentially enlargeable to press the axial end portion of the graft radially outwardly toward the body tissue surrounding the aperture, and the second substructure including a plurality of struts that are configured to extend substantially radially outwardly to engage the body tissue surrounding the aperture and hold the axial end portion of the graft in body-fluid-tight engagement with the side wall of the conduit annularly around the aperture, wherein the first substructure is resiliently biased to circumferentially enlarge to at least some degree by itself.